208 MAYAN CALENDAR SYSTEMS [eth. axn. 22 



Continuing our investigation of the data necessary to determine tlie 

 series, still referring to the one under consideration, we will next sup- 

 pose that the number of chucns can not be determined by inspection. 



Tlie terminal date being given — 12 Caban 5 Kayab (whicli falls in 

 a Ben year) — it is readily seen, by i-eference to Goodman's "Archaic 

 Annual Calendar." 51st year, or to my condensed calendar, that it 

 requires 17 days, counting bade, to reacli an Ahau whicli falls on the 

 8th day of the montli ((xoodman begins the count witli in Eb, Imt tliis 

 gives Ben as the 1st day of the month, and the result is tlie same), 

 lience the Ahau to be u.sed depends on the number of chuens — if 

 chuens 17 days, it will be — as seen by the table referred to — 8 j\.hau 

 8 Pax: if 1 cluien 17 days, th' n 1 Ahau 8 Mnan; if L'-17, then 7 Ahau 

 8 Kankiii; if 3-17, then 13 Ahau 8 Mac; if -t-17, then 6 Ahau 8 Ceh; 

 if 5-17, then 12 Ahau 8 Zac; if f',-l7, then 5 Ahau 8 Yax; if 7-17, then 

 11 Aliau 8 Chen; if 8-17, tlien 4 Ahaii 8 Mol; if 9-17, then 10 Ahau 8 

 Yaxliin; if 10-17, then 3 Ahau 8 Xul; if 11-17, then Aliau 8 Tzee; 

 if 12-17, then 2 Ahau 8 Zotz; if 13-17, then 8 Ahau 8 Zip; if 14-17, 

 then 1 Ahau 8 Uo; if 15-17, then 7 Ahau 8 Pop; if 10-17, then 9 Ahau 

 8 Cumhu; if 17-17, then 2 Ahaii 8 Kayab. The fact that Ahau is 

 the 8th day of the month in each case greatly limits the range of 

 possibilities. 



Suppose that, in addition to tlie terminal date, the numbers of 

 cycles and katuns are also known ('.i and 14 in this instance) ; the series 

 can be defluitelj' detei-miiu'd, and will be as given above. If the 

 numbers of cycles (9) and ahaus (13) are known and the number of 

 katuns is unknown, the series "54-9-14-13-4-17" will give the correct 

 date, but there is one oth»'i- — 53-9-1.3-13-13-17 — which will also give 

 the correct date, 12 Caban 5 Kayali. In this case the correct deter- 

 mination of the series depends on the initial day of the great cycle, to 

 wliicli attention will be called farther on. 



We next take the ease where, in addition to the dates and tlie 

 num1)er of days, the numbers of katuns and ahaus are known, and 

 the number of cycles is unknown. In the series under consideration 

 the niimber of katuns is 14, of ahaus 13. Tliese data are sufiBcient to 

 determine the series, and in this instance the result is as given above. 



The next intjuiry relates to the data necessary to determine the ter- 

 minal date where this can not be recognized by inspection, or where 

 that given is erroneous. Where neither the day noi- the day of the 

 month is known, it is necessary to have the entire numeral series — 

 that is, 54-9-14-13-4-17, in tlie example we liavebeen using — in order 

 to determine the date. If the day of tlie terminal date of the series 

 can be a.scertained by inspection, then the date can be determined 

 without knowing the number of days; thus 54-9-14-13-4-?, ? Caban 

 ? (month) will be sutticient to ascertain that this terminal date is 12 

 Caban 5 Kayab. Turning to Goodman's "Archaic Chronological 

 Calendar," 54th great c.Vcle, 9th cycle, 14tli katnii, 13th ahau, we find 



